a. ĐKXĐ : \(a\ge0;a\ne1;a\ne4;a\ne9\)
\(C=-\frac{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}{\sqrt{a}-1}-\frac{\left(\sqrt{a}-2\right)\left(a+2\sqrt{a}+4\right)}{\sqrt{a}-2}+\frac{\left(\sqrt{a}-2\right)\left(\sqrt{a}-3\right)}{\sqrt{a}-3}\)
\(=-\sqrt{a}-1-a-2\sqrt{a}-4+\sqrt{a}-2\)
\(=-a-2\sqrt{a}-7\)
b. \(C=-a-2\sqrt{a}-7\le-7\)
\(\text{Dấu }=\text{xảy ra }\Leftrightarrow a=0\)
c. \(a^2-3a=0\)
\(\Leftrightarrow a\left(a-3\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}a=0\\a=3\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}C=-7\\C=-10-2\sqrt{3}\end{matrix}\right.\)
d. \(C=-13\)
\(\Leftrightarrow-a-2\sqrt{a}-7=-13\)
\(\Leftrightarrow a+2\sqrt{a}-6=0\)
\(\Leftrightarrow\left[{}\begin{matrix}a=-1+\sqrt{7}\left(TM\right)\\a=-1-\sqrt{7}\left(\text{loại}\right)\end{matrix}\right.\)
\(\Leftrightarrow a=-1+\sqrt{7}\)
